David Spence: Cheating via Selective Up Card. For Don or Norm

[kc]

> OK, I'll take your word for it that this is harder
> than I thought. My idea was:

> 1. For each card from 2 to 9:
> a. Remove the card from the deck
> b. Proceed as normal except when it comes to playing
> out the dealer's hand, add the removed card first.
> 2. Average the EV's from 1 to come up with an overall
> strategy and edge.

> There are no more first card A/T than normal though,
> so this is no greater than the overall house edge.
> This is purely for interest's sake though, and to
> prove that such a method of cheating is a bad idea. So
> if you're not interested, don't worry about it.

I did this for a player hand of 10,6 vs 10. It would also need to be done for all player's other hands versus all other dealer up cards. If dealer does not flip up his first card, you know that it is a 2-9. His second card turns out to be a 10 and is the up card. You know that 1/8 of the time his hole card is 2 through 9 respectively, summarized below.

 

player hand is 10,6; dealer has an up card of 10 

Dealer hole card   hit EV     stand EV 

2                  -.4180     -.0593 

3                  -.4038     +.0215 

4                  -.3872     +.1184 

5                  -.3677     +.1862 

6                  -.3351     +.1667 

7                  -.2500     -1.000 

8                  -.4167     -1.000 

9                  -.5833     -1.000 

 

Average            -.3952     -.3208 

.
So you would better off by about 7.4% by going against basic strategy when dealer flips a 10 on his second card. Dealer would flip a 10 on his second card (32/52)(16/51) = .193 of the time.

Anyway, that's how I'd approach the problem. I'd have to add some new programming to my old program to make it workable though. My new program doesn't allow dealer hand types other than up card to be used at this time.

kc

[Magician]

>
> I did this for a player hand of 10,6 vs 10. It would
> also need to be done for all player's other hands
> versus all other dealer up cards. If dealer does not
> flip up his first card, you know that it is a 2-9. His
> second card turns out to be a 10 and is the up card.
> You know that 1/8 of the time his hole card is 2
> through 9 respectively, summarized below.
> player hand is 10,6; dealer has an up card of 10
> Dealer hole card hit EV stand EV
> 2 -.4180 -.0593
> 3 -.4038 +.0215
> 4 -.3872 +.1184
> 5 -.3677 +.1862
> 6 -.3351 +.1667
> 7 -.2500 -1.000
> 8 -.4167 -1.000
> 9 -.5833 -1.000
> Average -.3952 -.3208
> .
> So you would better off by about 7.4% by going against
> basic strategy when dealer flips a 10 on his second
> card. Dealer would flip a 10 on his second card
> (32/52)(16/51) = .193 of the time.
> Anyway, that's how I'd approach the problem. I'd have
> to add some new programming to my old program to make
> it workable though. My new program doesn't allow
> dealer hand types other than up card to be used at
> this time.
> kc

Excellent work. Looks like it would be a painful process to go through every hand like this though. Thanks for your time.

[kc]

>
> I did this for a player hand of 10,6 vs 10. It would
> also need to be done for all player's other hands
> versus all other dealer up cards. If dealer does not
> flip up his first card, you know that it is a 2-9. His
> second card turns out to be a 10 and is the up card.
> You know that 1/8 of the time his hole card is 2
> through 9 respectively, summarized below.
> player hand is 10,6; dealer has an up card of 10
> Dealer hole card hit EV stand EV
> 2 -.4180 -.0593
> 3 -.4038 +.0215
> 4 -.3872 +.1184
> 5 -.3677 +.1862
> 6 -.3351 +.1667
> 7 -.2500 -1.000
> 8 -.4167 -1.000
> 9 -.5833 -1.000
> Average -.3952 -.3208
> .
> So you would better off by about 7.4% by going against
> basic strategy when dealer flips a 10 on his second
> card. Dealer would flip a 10 on his second card
> (32/52)(16/51) = .193 of the time.
> Anyway, that's how I'd approach the problem. I'd have
> to add some new programming to my old program to make
> it workable though. My new program doesn't allow
> dealer hand types other than up card to be used at
> this time.
> kc

Actually, I made an error. Since there is a 6 in player's hand, the probability of his hole card being a 2,3,4,5,7,8,9 is 4/31 and the probability of it being a 6 is 3/31. I redid the computation:
hit EV =~ -.3972
stand EV =~ -.3365,
so player is better off standing by about 6.1%.

kc

[kc]

> Excellent work. Looks like it would be a painful
> process to go through every hand like this though.
> Thanks for your time.

OK, I added some new programming to my old CA and it appears you were right that proper strategy yields an advantage (~1%). It was kind of painful, but in the process I added a few other things that my new CA can't do as well.

The dealer is doing his best to display an up card of ace or ten in order to BBQ the player, but in the process is providing extra knowledge. EVs and proper strategy versus such a dealer are in link.

kc

HC Not A-T

[Magician]

> OK, I added some new programming to my old CA and it
> appears you were right that proper strategy yields an
> advantage (~1%). It was kind of painful, but in the
> process I added a few other things that my new CA
> can't do as well.

> The dealer is doing his best to display an up card of
> ace or ten in order to BBQ the player, but in the
> process is providing extra knowledge. EVs and proper
> strategy versus such a dealer are in link.

> kc

Excellent work. I believe this is the first time the correct strategy and overall advantage for this scenario has been presented.

By the way, 41297762 decks? Is that some kind of inifinite-deck-approximation approximation?

[kc]

> Excellent work. I believe this is the first time the
> correct strategy and overall advantage for this
> scenario has been presented.

> By the way, 41297762 decks? Is that some kind of
> inifinite-deck-approximation approximation?

41297762 decks is just the maximum number of decks my CA can address without a data overflow. You might call such a large number of decks a virtual infinite shoe.

kc

[kc]

I found an error in my overall EV, when the dealer selectively chooses his up card to be an ace or ten. (If his first card is ace or ten, that's the up card. Otherwise, the second card is the up card, whatever it is.) Anyway, the EV for this using best strategy is not better than normal, but worse. I didn't weight the cases where the ace/ten are up cards and it is known that the hole card is not an ace or ten. I needed to multiply by the probability of an initial non ace/ten. I weighted the cases where the up card was a non ace/ten right, though. I think the overweighting of hands such as hard 11 vs 10, which is very favorable if it is known that the hole card is a 2-9 made my original EV too high. I think the strategies are OK. The EV for single deck, S17, NDAS, is -0.46%. The EV for the same game unselectively dealt is -0.0147%, so the selective game is worse, not better.

kc

HCNotAT

[Librarian]

> Excellent work. I believe this is the first time the
> correct strategy and overall advantage for this
> scenario has been presented.

How can this thread go on for 50 posts without someone pointing out that Grosjean's book has an extensive discussion of Selective Upcard, along with other dealer cheating techniques. Edges and strategies are given.

[Norm Wattenberger]

I don't recall a discussion on these numbers in BC. But even if the exact question is answered somewhere; BC unfortunately makes for a poor reference. It would be cynical indeed to point someone to a book that was so limited in copies that you can't find it

> How can this thread go on for 50 posts without someone
> pointing out that Grosjean's book has an extensive
> discussion of Selective Upcard, along with other
> dealer cheating techniques. Edges and strategies are
> given.